On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality
In this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an applica...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/619623 |
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| _version_ | 1832559763625345024 |
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| author | G. A. Chechkin Yu. O. Koroleva L.-E. Persson P. Wall |
| author_facet | G. A. Chechkin Yu. O. Koroleva L.-E. Persson P. Wall |
| author_sort | G. A. Chechkin |
| collection | DOAJ |
| description | In this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results, the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated. |
| format | Article |
| id | doaj-art-5628f1728c6447f7a67061ec26b5adac |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-5628f1728c6447f7a67061ec26b5adac2025-02-03T01:29:12ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/619623619623On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type InequalityG. A. Chechkin0Yu. O. Koroleva1L.-E. Persson2P. Wall3Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, RussiaDepartment of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, RussiaNarvik University College, Postboks 385, 8505 Narvik, NorwayDepartment of Engineering Science and Mathematics, Luleå University of Technology, 971 87 Luleå, SwedenIn this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results, the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated.http://dx.doi.org/10.1155/2011/619623 |
| spellingShingle | G. A. Chechkin Yu. O. Koroleva L.-E. Persson P. Wall On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality International Journal of Differential Equations |
| title | On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality |
| title_full | On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality |
| title_fullStr | On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality |
| title_full_unstemmed | On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality |
| title_short | On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality |
| title_sort | on spectrum of the laplacian in a circle perforated along the boundary application to a friedrichs type inequality |
| url | http://dx.doi.org/10.1155/2011/619623 |
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